So it's not wrong when other people use the word, "God" in a way that implies that it is male living in another dimension that wants you to do its bidding and exists? Mass delusions exist which can make many people say the same wrong things.

Me saying someone is wrong is not what makes them wrong. It is the distinction between the words they use and the reality of the situation that makes them wrong. Me saying they are wrong is just representative of that truth, but is not what makes it true. — Harry Hindu

I don't understand what you're saying here.

Someone is wrong if they claim that God exists but they're not wrong if they claim that the word "God" means "creator deity" (or whatever).

And I don't understand how this relates to the topic under discussion. Are you saying that English-speaking people don't use the word "man" to refer to those whose gender is male (regardless of sex) or are you saying that people whose gender is male (regardless of sex) don't exist?

Relative to this alternative payout structure, your own Halfer reasoning is unnecessary. — Pierre-Normand

Yes, I have tried to argue this point several times. A rational person's credence in the outcome of the coin toss is unrelated to the betting strategy that yields the greater expected return in the long run, and is why any argument to the effect of "if I bet on Tails then I will win $2\over3$ bets, therefore my credence that the coin landed on Tails is $2\over3$" is a non sequitur. The most profitable betting strategy is established before being put to sleep when one’s credence is inarguably $1\over2$, showing this disconnect.

After waking up you just either believe that the coin most likely landed on Tails or you don't, and I think my extreme example shows that no rational person’s credence will be based on some counterfactual ratio of awakenings in the way that Thirders say. It seems absurd for anyone to answer anything other than $1\over{2^{100}}$, regardless of how you “choose” to interpret the question.

That's not what I said. I said that the idea that because language can evolve a certain way, doesn't mean it should. If English evolved rapidly into an ambiguous and locally defined set of terms and meanings in each state, we would have a difficult time talking to one another at all. Just because something can occur, doesn't mean its the best outcome for what language's purpose is.

...

Of course, I never denied this, nor does this address my point. What I'm noting is that there are more beneficial and less beneficial ways for language to evolve. Its a constant balance between clarity of communication, efficiency in effort, and applicability to a wider audience. Thus, it is not foolish to debate whether words should mean something. — Philosophim

What you literally said, and what I am replying to, was "the terms man and woman indicate a person's age and sex, not gender" and this is factually incorrect. The terms are sometimes used to indicate a person's sex and sometimes used to indicate a person's gender.

Whether or not you think they should be used this way, and whether or not I think the word "slay" should be used to mean "impressive", is irrelevant to the factual matter of how English-speaking people actually use these words.

According to you, so far, the trans community and its supporters are free to advocate for their particular language uses. But other people are not supposed to advocate for their own particular language uses — baker

I'm saying that words can have more than one meaning, and that one of the meanings of the word "man" is "someone whose gender is male".

I'm not sure what you mean by "advocating" for a particular language use. If you don't want to use the word "man" to mean "someone whose gender is male" or the word "slay" to mean "impressive", then don't. But to argue that these words don't also mean these things is factually incorrect. Such usages are sufficiently widespread that they count as alternative meanings and not (intentional or unintentional) misuses, e.g. using the word "cat" to mean "dog".

No, it is not foolish at all. That's the entire point of English class. Present participles, conjuctive disjunctions (What are you functions?) are all a means to ensure that we have stable rules and approaches to grammar and communication. Because the entire purpose of language is to clearly communicate a concept in a way that can be easily understood by other parties in the language without debate. — Philosophim

To paraphrase Captain Barbossa, they're more what you'd call guidelines than actual rules. And, once again, natural languages just aren't the perfectly logical, consistent, and unambiguous things you seem to want them to be.

The above paragraph is a prime example. You "shouldn't" start a sentence with a conjunction. Except I do it all the time.

And of course people will deny that words mean certain things. If I started calling the Big Bang God and told you, "You believe in God", you would have an issue. It is quite reasonable to debate why we should or should use certain language and meanings for those words. If I said "subjectivity" was actually the same definition as 'objectivity', there would be a lot of people on these forums telling me, "No, you're wrong". — Philosophim

Get enough people using a word in a different-than-normal way and its meaning changes. That's how languages evolve. Imagine how silly Shakespeare would seem if we brought him back to life and he bitched about us not speaking Ye Olde Englishe properly.

Earlier, you talked about being a fool for battling others on how to use words. Then, given your contibutions here, you must be talking about yourself ... — baker

It's foolish to argue that words should or shouldn't mean something, or to deny the empirical fact that they are used to mean certain things.

some people still believe that dictionaries should have a normative function — baker

Well, they don't. Even the Académie Française, which is putatively the "authority" on the French language, can't do this. Natural languages just aren't the sort of things that can be dictated in this way. You can pretend, or say "well, it's not recognized by such-and-such an organization" but why should anyone care about that? I'm going to continue to slay despite your protestations.

Not everyone uses it that way. And since there is in fact no divine dictionary, nothing is set in stone. And so the battle for the meaning of a word is ongoing. — baker

Not everyone uses the word "slay" to mean "impressive" (or whatever it means to youths these days), but that is nonetheless one of its meanings.

If you don't want to use the word "man" to refer to anyone whose gender is male, regardless of sex, then don't. But it's bizarre to suggest that other people are wrong if they do use it that way. It's prominent enough to warrant being considered another meaning.

Her Thirder-credence would then be pragmatically relevant to selecting the destination most likely to afford her a sunny trip. — Pierre-Normand

Again, there's not much sense in this so-called "pragmatically relevant" credence. Even before being put to sleep – and even before the die is rolled – I know both that the die is most likely to not land on a 6 and that betting that it did will offer the greater expected return in the long run. So after waking up I can – and will – continue to know that the die most likely did not land on a 6 and that betting that it did will offer the greater expected return in the long run, and so I will bet against my credence.

With respect to "pragmatic relevance", Thirder reasoning is unnecessary, so if there's any sense in it it must be somewhere else.

Under the Thirder interpretation, all three of those biconditionally related "experienced" events are actual on average 2/3 of the times that SB is experiencing a typical awakening episode. — Pierre-Normand

My argument is that a rational person should not – and would not – reason this way when considering their credence, and this is most obvious when I am woken up 2¹⁰¹ times if the coin lands heads 100 times in a row (or once if it doesn't).

It is true that if this experiment were to be repeated 2¹⁰¹ times then we could expect $2\over3$ of all awakenings to occur after the coin landed heads every time, but it's also irrelevant. The experiment is only performed once. I strongly believe that it is irrational for one's credence to consider this long term average; a rational person, after waking up and knowing that the experiment is only performed once, will only consider the sheer improbability of the coin landing heads every time. Their credence remains ${1\over{2^{100}}}$. There is no ambiguity in the question or the answer.

Thirder reasoning only has its place, if it has a place at all, if both a) the experiment is repeated 2¹⁰¹ times and b) Sleeping Beauty is also made to forget between experiments. It matters that the problem does not stipulate these two conditions.

I answered your question.

Your opening post shows that you understand the distinction between sex and gender, given that you use the phrases "female who expresses with male gender" and "male who expresses with female gender".

I am explaining to you that the English word "man" can mean "a person whose biological sex is male" and it can mean "a person whose gender is male".

Despite your apparent suggestion that words should only mean one thing, they sometimes don't. Natural languages are messy. Accept it.

It doesn’t have just one meaning. It can refer to sex or it can refer to gender. This isn’t to say that it is equally likely to refer to gender as sex.

And what does the word 'man' mean without those modifiers? — Philosophim

It's an umbrella term that includes cis men and trans men.

What do those modifiers mean when they're added to the base word 'man'? — Philosophim

A cis man is someone whose sex is male and gender is male. A trans man is someone whose sex is female and gender is male.

Yes, you logically said that. — Philosophim

No, I didn't. I said that the word "man" is used to refer to cis men and used to refer to trans men.

No, it is not an empirical fact that when people generally use the word man, that they are thinking it is equally as likely that it is an adult human female behaving like a man. — Philosophim

I didn't say that.

So i guess to increase her odds, she bets tails 100% of the time since she can't remember which phase of the experiment she's in, and the 2/3rds tailsers make a profit off the gambling? — ProtagoranSocratist

It doesn't increase her odds but it does increase her expected return in the long run.

On this point it's worth considering an extreme example I provided two years ago.

I am put to sleep and a coin is tossed 100 times. If it lands heads every time then I am woken up, interviewed, and put back to sleep 2¹⁰¹ times, otherwise I am woken up, interviewed, and put back to sleep once.

When being interviewed, I am asked a) my credence that the coin landed heads every time and b) to place a bet on the outcome.

All of these are true:

1. If I know that the experiment will be performed once
a. My credence is ${1\over{2^{100}}}$
b. I will bet that the coin did not land heads every time

2. If I know that the experiment will be performed 2¹⁰¹ times
a. My credence is ${1\over{2^{100}}}$
b. I will bet that the coin did land heads every time

I strongly believe that a perfectly rational agent like Sleeping Beauty will believe and do the same. Thirder reasoning seems to be that if (2b) results in twice as many successful bets then (1a) is false, and that simply doesn't follow, either for me or for Sleeping Beauty.

This ignores the definitions I've given above — Philosophim

It doesn't ignore it. I am simply explaining the empirical fact that your definition is inconsistent with how English speakers actually use the words.

You can argue that some word shouldn't mean something, but that's not the same as arguing that it doesn't mean that thing.

Whether you like it or not, the words "man" and "woman" are used to refer also to transmen and transwomen.

Correct, but good vocabulary should be clear, unambiguous, and logical. — Philosophim

No natural language is clear, unambiguous, and logical. Certainly not English. Maybe check out Loglan if that's your interest.

My question to you then is, "Why should we change the term man to mean gender instead of sex by default?" — Philosophim

There's nothing about language that we should do; there's just what we actually do. And what we actually do is use the word "man" to refer also to transmen.

I am noting that in the general context in regards to sex and gender, 'man' refers to a person's age and sex, not gender. — Philosophim

A word's meaning is determined by how its users use it. If a sufficient number of English speakers use the word "man" to refer to both trans men and cis men, fully recognising the biological differences between the two, then the word "man" refers to both sex and gender.

There's no divine dictionary that dictates what words mean.

The terms man and woman indicate a person's age and sex, not gender. — Philosophim

Words can mean more than one thing. The word "man" can also mean "human", and as a verb it refers to a certain kind of behaviour, e.g. in the phrase "man up".

In the shiny-penny case, fair pennies have a 1/2 chance to land Tails, but Tails pennies are twice as likely to be noticed. So among the pennies I actually notice, about 2/3 will be Tails. When I notice this penny, updating to (2/3) for Tails isn’t smuggling in a mysterious propensity; it’s just combining:

1) the base chance of Tails (1/2), and
2) the noticing rates (Tails noticed twice as often as Heads). — Pierre-Normand

You appear to be affirming the consequent. In this case, Tails is noticed twice as often because Tails is twice as likely to be noticed. It doesn't then follow that Tail awakenings happen twice as often because Tails awakenings are twice as likely to happen.

The Sleeping Beauty case in contrived in such a way that a Heads awakening is guaranteed to happen and two Tails awakenings are guaranteed to happen. This contrivance doesn't allow you to compare the likeliness of a Tails awakening compared to a Heads awakening.

1) Per run: most runs are 'non-six', so the per-run credence is P(6)=1/6 (the Halfer number).
2) Per awakening/observation: a 'six-run' spawns six observation-cases, a 'non-six' run spawns one. So among the observation-cases, 'six' shows up in a 6/5 ratio, giving P('six'|Awake)=6/11 (the Thirder number). — Pierre-Normand

This doesn't make sense.

She is in a Tails awakening if and only if she is in a Tails run.
Therefore, she believes that she is most likely in a Tails awakening if and only if she believes that she is most likely in a Tails run.
Therefore, her credence that she is in a Tails awakening equals her credence that she is in a Tails run.

You can't have it both ways.

Since she is only being rewarded with £100 for each sequence of six successful bets — Pierre-Normand

This isn't what's happening. There is only a single bet, placed before she is put to sleep. She is then given a 3 hour window in which she is able to change her bet, and can do so as many times as she likes. The same for Prince Charming, although he is never put to sleep.

In this situation, if either of their credences in the outcome genuinely changed to favour the die landing on a 6 then they would change their bet. Prince Charming does this when he learns that his die is loaded. So why doesn't Sleeping Beauty after having her memory wiped? Because despite Thirder word games, her credence in the outcome hasn't genuinely changed. She continues to know that if she changes her bet then she is most likely to lose.

If it helps, it's not a bet but a holiday destination. The die is a magical die that determines the weather. If it lands on a 6 then it will rain in Paris, otherwise it will rain in Tokyo. Both Prince Charming and Sleeping Beauty initially decide to go to Paris. If after being woken up Sleeping Beauty genuinely believes that the die most likely landed on a 6 then she genuinely believes that it is most likely to rain in Paris, and so will decide instead to go to Tokyo.

So, there are three "events" at issue: the coin toss, that occurs before the experiment, the awakenings, and the runs. — Pierre-Normand

But again, the paradox is only a paradox if the $H$ in $P(H|Awake) = {1\over3}$ denotes the same event as the $H$ in $P(H) = {1\over2}$.

The paradox is: this awakening gives me reason to believe that this coin toss most likely landed on a tails.

If this claim is false then Halfers are right and Thirders are either wrong or equivocating.

Apologies for doing this as a second post. I did mean to include this earlier but miss-clicked.

Of course, one salient disanalogy between this penny drop analogy and the SB problem is that, in the standard SB problem, each coin is being tracked separately and noticed at least once, on Monday. But I don't think this disanalogy undermines the main point. It's because tail-outcomes causally increase the proportion of awakening episodes at which SB would encounter them that, on each occasion where she encounters them, SB can update her credence that the coin landed Tails. That this rational ground for Bayesian updating remains valid even in cases of singular experimental runs with amnesia (as in the original SB problem) is something that I had illustrated by means of a Christmas gift analogy (see the second half of the post). — Pierre-Normand

I think your comment sidestepped the issue I was raising (or at least misunderstood it, unless I'm misunderstanding you), but this reference to Bayesian probability will make it clearer.

Everyone agrees that $P(H) = {1\over2}$.

Halfers claim that $P(H|Awake) = {1\over2}$ and Thirders claim that $P(H|Awake) = {2\over3}$.

You claim that both Halfers and Thirders are right because they are referring to different events, which I understand to mean that the $H$ in $P(H|Awake) = {1\over2}$ and the $H$ in $P(H|Awake) = {2\over3}$ do not designate the same event, which means that one or both do not designate the same event as the $H$ in $P(H) = {1\over2}$.

The problem is only a problem (or paradox) if the $H$ in $P(H|Awake) = {2\over3}$ designates the same event as the $H$ in $P(H) = {1\over2}$, and so it cannot be that both Halfers and Thirders are right. One may be "right" in isolation, but if used in the context of this paradox they are equivocating, and so are wrong in the context of this paradox.

The SB setup is a very close analogy to this. Coins landing Tails play a similar causal role. Just replace "increased proclivity to being noticed by a passerby" with "increased proclivity to awaken a random test subject in the Sleeping Beauty Experimental Facility". — Pierre-Normand

This, I think, shows the fallacy. You're equivocating, or at least begging the question. It's not that there is an increased proclivity to awaken in this scenario but that waking up in this scenario is more frequent.

In any normal situation an increased frequency is often explained by an increased proclivity, but it does not then follow that they are the same or that the latter always explains the former – and this is no normal situation; it is explicitly set up in such a way that the frequency of us waking up Sleeping Beauty does not mirror the probability of the coin toss (or die roll).

If you are allowed to place 6 bets if the die lands on a 6 but only 1 if it doesn't then it is both the case that winning bets are more frequently bets that the die landed on a 6 and the case that the die is most likely to not land on a 6.

it's rational to bet on the least likely outcome (namely, a non-six result, which occurs only 5/11th of the times) since this is the betting behavior that maximizes the expected return. In fact, it could be argued that this arbitrary payoff structure is misleading in the present context since it is being designed precisely to incentivise the bettor to bet on the least likely outcome according to their own credence. — Pierre-Normand

The multiple bets structure is the misleading structure, and where one is betting on the least likely outcome. If you are offered the opportunity to place six bets that the die landed on a 6 or one bet that it didn’t, what do you do? You place six bets that the die landed on a 6 even though your credence that it did is $1\over6$. Nothing changes after being made to forget before any bet and so you remain committed to what you knew before being put to sleep.

The single bet structure (why do you call it “arbitrary”?) is the appropriate structure to properly assess the problem: does being put to sleep and woken up change her credence in the die roll, like Prince Charming being told that his die is loaded? If it did then she would follow his lead and change her bet, and we would have a genuine paradox (although she'd lose money). If she doesn’t then her credence hasn’t changed and the problem is resolved in the Halfer’s favour (more on this below).

It's the (well defined) credence in combination with the payoff structure that jointly govern the rational betting behavior. — Pierre-Normand

Yes, so consider the previous argument:

P1. If I keep my bet and the die didn't land on a 6 then I will win £100 at the end of the experiment
P2. If I change my bet and the die did land on a 6 then I will win £100 at the end of the experiment
P3. My credence that the die landed on a 6 is $6\over11$
C1. Therefore, the expected return at the end of the experiment if I keep my bet is £$n$
C1. Therefore, the expected return at the end of the experiment if I change my bet is £$m$

What values does she calculate for $n$ and $m$?

She multiplies her credence in the event by the reward. Her calculation is:

C1. Therefore, the expected return at the end of the experiment if I keep my bet is £45.45
C2. Therefore, the expected return at the end of the experiment if I change my bet is £54.55

This is exactly what Prince Charming does given his genuine commitment to P3 and is why he changes his bet.

So why doesn’t she change her bet? Your position requires her to calculate that $n \gt m$ but that’s impossible given P1, P2, and P3. She can only calculate that $n \gt m$ if she rejects P3 in favour of “my credence that the die landed on a 6 is $1\over6$”.

I’ll respond to the other comment this evening after work.

You seem to continue to conflate an outcome's expected return with its probability and assert that one's behaviour is only governed by one's credence in the outcome. Neither of these things is true. I've shown several times that the least likely outcome can have the greater expected return and so that this assessment alone is sufficient to guide one's decisions. No number of analogies is going to make either "she wins two thirds of the time if she acts as if A happened, therefore she believes (or ought to believe) that A most likely happened" or "she believes that A most likely happened, therefore she acts (or ought to act) as if A happened" valid inferences.

But the most important part of my previous comment were the first two paragraphs, especially when considering the standard problem.

those credences target differently individuated events — Pierre-Normand

This is where I believe the mistake is made. The question she is asked after being woken up is the same question she is asked before being put to sleep. There is no ambiguity in that first question, and so there is no ambiguity in any subsequent question. There is a single event that is the target of the question before being put to sleep and we are asking if being put to sleep and woken up gives Sleeping Beauty reason to re-consider her credence in that event, much like Prince Charming re-considers his credence in that event after being told that his coin is loaded. Neither Sleeping Beauty nor Prince Charming is being asked to consider their credence in one of two different events of their own choosing.

Indeed, and, as previously explained, that because Halfers and Thirders are typically talking past each other. They're not talking about the same events. — Pierre-Normand

Which is why I think that Thirders have fabricated a problem that doesn't exist and Halfers are right. The problem only arises because it is suggested that Sleeping Beauty's credence in Event A changes after being put to sleep and woken up, despite no new information. All I can gather from your responses is that Thirders say that Sleeping Beauty's credence in Event B is $2\over3$. But we're not interested in Sleeping Beauty's credence in Event B; we're only interested in Sleeping Beauty's continued credence in Event A.

Remember the flip-coin scenario where the singular H-awakenings take place in the West-Wing of the Sleeping Beauty Experimental Facility and the dual T-awakenings are taking place in the East-Wing. The West-Wing is surrounded by a moat with crocodiles and the East-Wing is surrounded by a jungle with lions. On the occasion of her awakening Sleeping Beauty finds a rare opportunity to escape and can either choose to bring a torch (that she can use to scare off lions) or a wooden plank (that she can use to safely cross the moat). A Thirder analysis of the situation is natural in that case since it tracks singular escape opportunities. Her credence that she will encounter crocodiles is 2/3 (as is her credence that the coin landed Tails). Taking the plank is the safest bet and, indeed, two thirds of Sleeping Beauties who make this bet on the rare occasions where this opportunity presents itself to them survive. — Pierre-Normand

That you're more likely to escape if you assume that the coin landed tails isn't that the coin most likely landed tails. You just get two opportunities to escape if the coin landed tails. It's exactly the same as being able to place either two bets on outcome A or one bet on outcome B, and where P(A) <= P(B) but P(B) < 2P(A). It is more profitable to bet twice on the least probable outcome than once on the most probable outcome. You don't need to force yourself to believe that outcome A is more probable to justify placing those bets. The expected return already does that for you.

Those two reasonings concern the same dice but two different statements of credence in two different kinds of events/outcomes. — Pierre-Normand

This makes no sense. There is only one kind of event; being woken up after a die roll. Her credence in the outcome of that die roll cannot be and is not determined by any betting rules. Maybe she's not allowed to place a bet at all

After waking up, either she continues to believe that the probability that the die landed on a 6 is 1/6, as Halfers say, or she now believes that it is 6/11, as Thirders say.

Only then, if allowed, can she use her credence to calculate the expected returns of placing or changing a bet, accounting for the particular betting rules. And as I believe I showed above, only a credence of 1/6 provides a consistent and sensible approach to both betting scenarios.

It's not an arbitrary payout structure.

A £100 reward is paid out at 6:00pm for any correct bet on the outcome of a die roll. Sleeping Beauty and Prince Charming each bet that their die will not land on a 6. They are both free to change their bet at any time before 6:00pm, e.g. if something happens to affect their credence in the outcome, and can do so as many times as they like. Neither of them has a watch.

Sleeping Beauty is told that if her die landed on a 6 then she will be put to sleep and woken up at six arbitrary points before 6:00pm, otherwise she will be put to sleep and woken up at one arbitrary point before 6:00pm.

Prince Charming is told before 6:00pm that his die is loaded and that the probability that it landed on a 6 is $6\over11$.

It doesn’t make any sense to argue that Sleeping Beauty (after being put to sleep and woken up) and Prince Charming (after being told that his die is loaded) come to share the same credence in the outcome of their die roll but that only he changes his bet. If she truly shares his credence then she would also change her bet.

A six is the most likely outcome, so I'm betting on it. — Pierre-Normand

A six is the least likely outcome, but has the highest expected return, and so she bets on it. Her reasoning both before being put to sleep and after being woken up is:

P1. If I always bet that the die didn't land on a 6 and it didn't then I will win £100 at the end of the experiment (1 × £100 bet)
P2. If I always bet that the die did land on a 6 and it did then I will win £600 at the end of the experiment (6 × £100 bets)
P3. The probability that the die did land on a 6 is $1\over6$
C1. Therefore, the expected return if I always bet that the die didn't land on a 6 is £83.33
C2. Therefore, the expected return if I always bet that the die did land on a 6 is £100
C3. Therefore, the expected return if I always bet that the die did land on a 6 is $6\over11$
C4. Therefore, I will always bet that the die did land on a 6

Her credence remains committed to P3, else she’d calculate very different expected returns after being put to sleep and woken up.

A thirder will not agree with A4 or A5. — Pierre-Normand

Correct. Her reasoning would be:

A1. If I keep my bet and the die didn't land on a 6 then I will win £100
A2. If I change my bet and the die did land on a 6 then I will win £100
A3. My credence that the die landed on a 6 is $6\over11$
A4. Therefore, the expected return if I keep my bet is £45.45
A5. Therefore, the expected return if I change my bet is £54.55

And yet you say she doesn't change her bet even though she has calculated that changing her bet is more profitable? There's something amiss with your reasoning.

Either she does change her bet or her credence that the die landed on a 6 continues to be $1\over6$.

All this shows is that the lopsided payout structure makes it irrational for her to bet on the most likely outcome. — Pierre-Normand

Again, you have it backwards. The most likely outcome is always that the die didn't land on a 6, but when she is allowed to place multiple bets it is irrational to bet on the most likely outcome.

If I can place one bet on a single outcome with $5 \over 6$ odds or 6 bets on a single outcome with $1 \over 6$ odds, the latter has the highest expected return even though it has the lowest odds. I don't even have to be put to sleep and woken up to do this. I can just say before the experiment starts that I choose to place 6 bets that the die will land on a 6 instead of 1 bet that it won't.

However, owing to the fact that the traveller must establish their credence on the occasion of encountering one among a set of indistinguishable doors, and 2/3rds of such doors belong to two-door dwellings, their credence that this house that they now are facing is a two-door dwelling is 2/3. — Pierre-Normand

That doesn't follow. It depends on the manner in which the door is chosen. Compare with a red bag containing 100 balls and a blue bag containing 50 balls. You "encounter" a ball. What is the probability that it came from the red bag? Is it $2\over3$ because $2\over3$ of the balls come from the red bag? Not if one "encounters" a ball by putting one's hand in a bag at random, as the probability that one picks the red bag is $1\over2$.

So you need to first specify the mechanism by which one has "encountered" a door, and this mechanism must be comparable to the Sleeping Beauty scenario for it to be an apt analogy.

Sorry, I deleted that post because it's late and I'm tired and I may have messed up the specific numbers. The general gist is what I said before. Your argument is that her reasoning after being woken up is:

A1. If I keep my bet and the die didn't land on a 6 then I will win £100
A2. If I change my bet and the die did land on a 6 then I will win £100
A3. My credence that the die landed on a 6 is $6\over11$
A4. Therefore, the expected return if I keep my bet is £83.33
A5. Therefore, the expected return if I change my bet is £16.67

But A3, A4, and A5 are inconsistent. If A3 really was true then she would calculate different values for A4 and A5, concluding that it is profitable to change her bet. But she doesn't do this.

You can't have it both ways. Either she genuinely believes it to be more likely that the die landed on a 6, and so she changes her bet, or she continues to believe it to be more likely that it didn't, and so she keeps her bet.

This is your favored interpretation. — Pierre-Normand

My "favoured" interpretation is the literal interpretation; she is being asked about the probability that a die rolled a six.

She isn't being asked about the long-term average frequency of being woken up when the die did land on a 6 and she isn't being asked about the long-term average frequency of experiencing a series of six successive awakenings when the die did land on a 6. Either of these two questions gives the same answer when asked before being put sleep as when asked after being woken up, and so there would be no problem to solve.

The problem only exists when the question being answered before being put sleep is the same question being answered after being woken up, and where the answer (allegedly) changes despite (apparently) no new information.

If the Thirder's answer before being put to sleep is $1\over6$ and if their answer after being woken up is $6\over11$ then either they are not answering the same question or one of their answers is wrong. And it is obvious in context that the correct answer to the question being asked before being put to sleep is $1\over6$.

The reason why SB can take a thirder rather than a halfer stance regarding her current awakening episode is because she may care about the long-term average frequency of such events (6-awakenings) — Pierre-Normand

She isn't being asked "what is the long-term average frequency of being woken up when the die did land on a 6?" Her answer to that question is the same both before being put to sleep and after being woken up, and so there wouldn't be a problem to solve.

The problem only exists because there is the counter-intuitive suggestion that her credence in the outcome of a die roll changes, comparable to being told that the die is loaded, after being woken up despite prima facie not being provided with any new information.

The actual question she is being asked is "what is the probability that the die did land on a 6?" which is the same as being asked for the value of $n$ below:

1. If I correctly bet that the die didn't land on a 6 then I will win £$a$
2. If I correctly bet that the die did land on a 6 then I will win £$b$
3. The probability that the die did land on a 6 is $n$
4. Therefore, the expected return if I bet that the die didn't land on a 6 is £$x$
5. Therefore, the expected return if I bet that the die did land on a 6 is £$y$

There is only one correct value for $n$ and that value is the value that gives the correct values for $x$ and $y$ – which is $1\over6$ both before being put to sleep and after being woken up.

Whereas if she were told that the die is loaded then the values of $n$, $x$, and $y$ all change and with it her actual credence in the outcome of the die roll.

You have it backwards. It's not that her credence changes and she bets against it when she can only place a single bet; it's that her credence doesn't change and she bets against it when she can place multiple bets.

Her reasoning after waking up when she can only place a single bet is:

A1. If I keep my bet and the die didn't land on a 6 then I will win £100
A2. If I change my bet and the die did land on a 6 then I will win £100
A3. The probability that the die landed on a 6 is $1\over6$
A4. Therefore, the expected return if I keep my bet is £83.33
A5. Therefore, the expected return if I change my bet is £16.67
A6. Therefore, the expected return if I keep my bet is $5\over6$
A7. Therefore, I will keep my bet

And her reasoning after waking up when she can place multiple bets is:

B1. If I always bet that the die didn't land on a 6 and it didn't then I will win £100
B2. If I always bet that the die did land on a 6 and it did then I will win £600
B3. The probability that the die landed on a 6 is $1\over6$
B4. Therefore, the expected return if I always bet that the die didn't land on a 6 is £83.33
B5. Therefore, the expected return if I always bet that the die did land on a 6 is £100
B6. Therefore, the expected return if I always bet that the die did land on a 6 is $6\over11$
B7. Therefore, I will bet that the die did land on a 6

Whereas your argument appears to be that her reasoning after waking up when we can only place a single bet is:

C1. If I keep my bet and the die didn't land on a 6 then I will win £100
C2. If I change my bet and the die did land on a 6 then I will win £100
C3. The probability that the die landed on a 6 is $6\over11$
C4. Therefore, the expected return if I keep my bet is £83.33
C5. Therefore, the expected return if I change my bet is £16.67
C6. Therefore, the expected return if I keep my bet is $5\over6$
C7. Therefore, I will keep my bet

Which makes no sense at all. If she truly believes C3 then she would have calculated different expected returns and changed her bet, just as you or I would if we came to learn that the die is loaded in favour of landing on a 6. But waking up doesn't function like learning that the die is loaded in favour of landing on a 6, and so her credence in the outcome doesn't change. Her credence is always that the probability that the die landed on a 6 is $1\over6$, consistent with common sense and explaining why she bets the way she does in both betting scenarios.

Thirder reasoning appears to conflate B6 and C3, which is both a mistake and a contradiction given B3.

Therefore, the "bet" one ought to make doesn't straightforwardly track one's credence in the outcome of the die roll, but rather, it must take into account the rules of payout in this specific experimental setup. — Pierre-Normand

If each outcome has the same reward then it is rational to bet on the most probable outcome.

Therefore, if her credence that the die landed on a 6 is $6\over11$ then she will change her bet. Therefore, if she doesn't change her bet then her credence that the die landed on a 6 isn't $6\over11$.

I guess you disagree with my notion, right? — javi2541997

I’m saying that your argument is fallacious.

Either it’s a non sequitur because “therefore X exists” does not follow from “I dreamed of X” or it begs the question because you’ve independently assumed that X exists (and in which case your dream is irrelevant).

Meanwhile, Michael or Javi is real — javi2541997

You’re begging the question.

Your argument is now “if I dream of X and if X exists then X exists”.

My dream was based on the experience of interacting with other living beings like me, not deities or gods. I believe that addresing Zeus is not particularly relevant to the existence of you, me, and the other members of this forum. — javi2541997

You’re arguing that dreaming of X is proof that X exists.

If the argument fails when X is Zeus then it fails when X is Michael.

Even if I was in a dream, my ability to have these thoughts, including interacting with you, proved your existence. — javi2541997

Does dreaming of Zeus prove that Zeus exists?

We could give them South Carolina. — frank

As a Brit, the only states I know are California (Hollywood), New York (the city), Florida (palm trees), Texas (cowboys), Alaska (cold), and Hawaii (those flower necklace things).

Ukraine will voluntarily cede some territories to Russia, for example Balakliia and Izium — Linkey

How about the USA cedes territory to Russia?

A way to resolve the PSR problem is to give a sufficient reason for the existence of humans and the universe, and there is nothing to require that the reason be a cause. The reason could be a purpose — Hanover

This makes no sense.

"Humans exist because Martians intend to use us as food" is a non sequitur, whereas "humans exist because Martians created Adam and Eve in a lab and set them loose on Earth" isn't.

I think your reasoning stems from the fact that the word "reason" can be used to refer to both the "how" (e.g. "Martians created us in a lab") and the "why" (in the sense of motivation, e.g. "Martians intend to use us as food"), but to equate the two is to equivocate.